The velocity $v(t)$ of a particle moving in one dimension is given by:

$$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T / 3 \\ \alpha T / 3, & T / 3 \leq t \leq 2 T / 3 \\ \alpha(T-t), & 2 T / 3 \leq t \leq T\end{cases} $$

where $\alpha(\neq 0)$ is a constant. What is the displacement of the particle from time $t=0$ to $T$ ?